There is nothing for your site URL that is coded into DT Register at all. This would be entirely an issue of your actual Joomla install and/or your menu item itself.
Check your configuration.php file and make sure the entries for live_site, log_path, and tmp_path are all correct. Mostly likely, after a change like this, these entries are wrong.
Also... if you are using a 3rd party SEF component, it may have some hard-coded URLs saved, and if one is associated with your DT Register menu item, then that could be an issue also.
Nathan is no longer affiliated with DTH since the recent acquisition. You can connect with him and get any type of Joomla website help at
www.JoomlaEmployee.com
.